If z_1, z_2, z_3, z_4 are the roots of the eq | vedclass

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(C) Let $P(z) = z^4 + z^3 + z^2 + z + 1 = (z - z_1)(z - z_2)(z - z_3)(z - z_4)$.We want to find the value of $\prod_{i=1}^{4} (z_i + 2)$.Note that $\p

Vedclass · Accepted Answer

$11$

Vedclass · Answer

(C) Let $P(z) = z^4 + z^3 + z^2 + z + 1 = (z - z_1)(z - z_2)(z - z_3)(z - z_4)$.We want to find the value of $\prod_{i=1}^{4} (z_i + 2)$.Note that $\prod_{i=1}^{4} (z_i + 2) = (-1)^4 \prod_{i=1}^{4} (-2 - z_i) = P(-2)$.Substituting $z = -2$ into the polynomial $P(z)$:$P(-2) = (-2)^4 + (-2)^3 + (-2)^2 + (-2) + 1$$P(-2) = 16 - 8 + 4 - 2 + 1$$P(-2) = 11$.Therefore,the product is $11$.

If $z_1, z_2, z_3, z_4$ are the roots of the equation $z^4 + z^3 + z^2 + z + 1 = 0$,then $\prod_{i=1}^{4} (z_i + 2)$ is equal to:

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